Barca headed into the contest at Camp Nou six points adrift of leaders Madrid, but appeared on track to close the gap when Luis Suarez put the hosts ahead early in the second half.
Lionel Messi and Neymar wasted fine opportunities to extend Barca's lead and the misses proved costly when Sergio Ramos headed home a 90th-minute equaliser.
It was a result that left Enrique exasperated at Barca's failure to secure all three points and believes there is no more room for error if they want to overhaul Zinedine Zidane's men.
"In the second half we were able to find our players between the lines much more easily," he told reporters in his post-match media conference.
"I think we controlled the game; we didn't suffer in any transitions by Real Madrid. There were two clear chances for Leo and Neymar, but we can't really talk about justice in football.
"It's all about scoring. In the last few minutes it was more down to Real needing to score.
"We need to improve our performances, especially at home to get more points because we are a long way from where we want to be.
"The game is played until the final minute - we had it in our hands but it wasn't to be. The only chance we have of overturning this [Madrid's six-point lead] is winning all our remaining games.
"If the game finished in the 89th minute we'd all be happy, but I'm not going to answer hypothetical questions.
"We were superior and I don't think football was fair to us, but we could improve every aspect [of our play].
"That's why we are ambitious. We could improve every aspect. If you look at the numbers [in the league table] it is obvious we are very far off where we need to be to be champions."